Existence and multiplicity of periodic solutions and subharmonic solutions for a class of elliptic equations
نویسندگان
چکیده
This paper focuses on the following elliptic equation { − u ′′ − p(x)u = f(x,u), a.e. x ∈ [0, l], u(0) − u(l) = u ′(0) − u ′(l) = 0, where the primitive function of f(x,u) is either superquadratic or asymptotically quadratic as |u| → ∞, or subquadratic as |u| → 0. By using variational method, e.g. the local linking theorem, fountain theorem, and the generalized mountain pass theorem, we establish the existence and multiplicity results for the periodic solution and subharmonic solution. c ©2017 All rights reserved.
منابع مشابه
Existence and multiplicity of positive solutions for a class of semilinear elliptic system with nonlinear boundary conditions
This study concerns the existence and multiplicity of positive weak solutions for a class of semilinear elliptic systems with nonlinear boundary conditions. Our results is depending on the local minimization method on the Nehari manifold and some variational techniques. Also, by using Mountain Pass Lemma, we establish the existence of at least one solution with positive energy.
متن کاملExistence of ground state solutions for a class of nonlinear elliptic equations with fast increasing weight
This paper is devoted to get a ground state solution for a class of nonlinear elliptic equations with fast increasing weight. We apply the variational methods to prove the existence of ground state solution.
متن کاملExistence and multiplicity of positive solutions for a coupled system of perturbed nonlinear fractional differential equations
In this paper, we consider a coupled system of nonlinear fractional differential equations (FDEs), such that both equations have a particular perturbed terms. Using emph{Leray-Schauder} fixed point theorem, we investigate the existence and multiplicity of positive solutions for this system.
متن کاملExistence of triple positive solutions for boundary value problem of nonlinear fractional differential equations
This article is devoted to the study of existence and multiplicity of positive solutions to a class of nonlinear fractional order multi-point boundary value problems of the type−Dq0+u(t) = f(t, u(t)), 1 < q ≤ 2, 0 < t < 1,u(0) = 0, u(1) =m−2∑ i=1δiu(ηi),where Dq0+ represents standard Riemann-Liouville fractional derivative, δi, ηi ∈ (0, 1) withm−2∑i=1δiηi q−1 < 1, and f : [0, 1] × [0, ∞) → [0, ...
متن کاملExistence of three solutions for a class of fractional boundary value systems
In this paper, under appropriate oscillating behaviours of the nonlinear term, we prove some multiplicity results for a class of nonlinear fractional equations. These problems have a variational structure and we find three solutions for them by exploiting an abstract result for smooth functionals defined on a reflexive Banach space. To make the nonlinear methods work, some careful analysis of t...
متن کامل